Dergiler / Turkish Journal of Mathematics / 2010 / Cilt: 34 - Sayı: 4
Complete systems of differential invariants of vector fields in a euclidean space
- Sayfa
- 543–559
- DOI
- —
Özet
The system of generators of the differential field of all G-invariant differential rational functions of a vector field in the n-dimensional Euclidean space Rn is described for groups G=M(n) and G=SM(n), where M(n) is the group of all isometries of Rn and SM(n) is the group of all euclidean motions of Rn. Using these results, vector field analogues of the first part of the Bonnet theorem for groups Aff(n), M(n), SM(n) in Rn are obtained, where Aff(n) is the group of all affine transformations of Rn. These analogues are given in terms of the first fundamental form and Christoffel symbols of a vector field.
Abstract
The system of generators of the differential field of all G-invariant differential rational functions of a vector field in the n-dimensional Euclidean space Rn is described for groups G=M(n) and G=SM(n), where M(n) is the group of all isometries of Rn and SM(n) is the group of all euclidean motions of Rn. Using these results, vector field analogues of the first part of the Bonnet theorem for groups Aff(n), M(n), SM(n) in Rn are obtained, where Aff(n) is the group of all affine transformations of Rn. These analogues are given in terms of the first fundamental form and Christoffel symbols of a vector field.